Variational quantum algorithms for trace norms and their applications

Li, Shengjie; Liang, Jin‐Min; Shen, Shu-Qian; Li, Ming

doi:10.1088/1572-9494/ac1938

Cited by 7 publications

(2 citation statements)

References 54 publications

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“…In quantum information theory and quantum many-body systems, it is important to distinguish quantitatively two different states [1][2][3][4][5][6][7]. To differentiate two states with density matrices ρ and ρ , one may compare the expectations values of some specific local or nonlocal operator δ O = O ρ − O ρ .…”

Section: Introductionmentioning

confidence: 99%

Subsystem distances between quasiparticle excited states

Zhang

Rajabpour

2022

J. High Energ. Phys.

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We investigate the subsystem Schatten distance, trace distance and fidelity between the quasiparticle excited states of the free and the nearest-neighbor coupled fermionic and bosonic chains and the ferromagnetic phase of the spin-1/2 XXX chain. The results support the scenario that in the scaling limit when one excited quasiparticle has a large energy it decouples from the ground state and when two excited quasiparticles have a large momentum difference they decouple from each other. From the quasiparticle picture, we get the universal subsystem distances that are valid when both the large energy condition and the large momentum difference condition are satisfied, by which we mean each of the excited quasiparticles has a large energy and the momentum difference of each pair of the excited quasiparticles is large. In the free fermionic and bosonic chains, we use the subsystem mode method and get efficiently the subsystem distances, which are also valid in the coupled fermionic and bosonic chains if the large energy condition is satisfied. Moreover, under certain limit the subsystem distances from the subsystem mode method are even valid in the XXX chain. We expect that the results can be also generalized for other integrable models.

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Section: Introductionmentioning

confidence: 99%

Subsystem distances between quasiparticle excited states

Zhang

Rajabpour

2022

J. High Energ. Phys.

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“…Actually, if just consider the completeness, we can use a VQA technique shown in Ref. [52] after our second sub-algorithm. (ii) The complexity of our algorithm is less than the complexity of VQNPE, even without considering the complexity of the third sub-algorithm of VQNPE.…”

Section: The Total Complexity and Discussionmentioning

confidence: 99%

Quantum algorithm for neighborhood preserving embedding

et al. 2022

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Neighborhood Preserving Embedding (NPE) is an important linear dimensionality reduction technique that aims at preserving the local manifold structure. NPE contains three steps, i.e., finding the nearest neighbors of each data point, constructing the weight matrix, and obtaining the transformation matrix. Liang et al. proposed a variational quantum algorithm (VQA) for NPE [Phys. Rev. A 101, 032323 (2020)]. The algorithm consists of three quantum sub-algorithms, corresponding to the three steps of NPE, and was expected to have an exponential speedup on the dimensionality n. However, the algorithm has two disadvantages: (1) It is not known how to efficiently obtain the input of the third sub-algorithm from the output of the second one. (2) Its complexity cannot be rigorously analyzed because the third sub-algorithm in it is a VQA. In this paper, we propose a complete quantum algorithm for NPE, in which we redesign the three sub-algorithms and give a rigorous complexity analysis. It is shown that our algorithm can achieve a polynomial speedup on the number of data points m and an exponential speedup on the dimensionality n under certain conditions over the classical NPE algorithm, and achieve significant speedup compared to Liang et al.’s algorithm even without considering the complexity of the VQA.

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Solving the Fully Entangled Fraction on Near-Term Quantum Devices

Liu

Wang

et al. 2023

Int J Theor Phys

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Variational quantum algorithms for trace norms and their applications

Cited by 7 publications

References 54 publications

Subsystem distances between quasiparticle excited states

Subsystem distances between quasiparticle excited states

Quantum algorithm for neighborhood preserving embedding

Solving the Fully Entangled Fraction on Near-Term Quantum Devices

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